Part $2$: A problem from previous midterm exam

Assume we have a computer with $6$ bits in one word and the signed $2\text{'}$s complement number system is used. Answer the following questions:

$($a$)$ Convert decimal number $-33$ into the corresponding $6-$bit binary number.

$($b$)$ Perform $(10)+(25)$ using the binary number system. Note that $10$ and $25$ are decimal numbers.

$($c$)$ Perform $(10)-(25)$ using the binary number system. Note that $10$ and $25$ are decimal numbers.

$($d$)$ Perform $(10)-(-25)$ using the binary number system. Note that $10$ and $-25$ are decimal numbers.